Results 1  10
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30
Optimizing binary MRFs via extended roof duality
 In Proc. CVPR
, 2007
"... Many computer vision applications rely on the efficient optimization of challenging, socalled nonsubmodular, binary pairwise MRFs. A promising graph cut based approach for optimizing such MRFs known as “roof duality” was recently introduced into computer vision. We study two methods which extend t ..."
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Cited by 171 (12 self)
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Many computer vision applications rely on the efficient optimization of challenging, socalled nonsubmodular, binary pairwise MRFs. A promising graph cut based approach for optimizing such MRFs known as “roof duality” was recently introduced into computer vision. We study two methods which extend this approach. First, we discuss an efficient implementation of the “probing ” technique introduced recently by Boros et al. [5]. It simplifies the MRF while preserving the global optimum. Our code is 400700 faster on some graphs than the implementation of [5]. Second, we present a new technique which takes an arbitrary input labeling and tries to improve its energy. We give theoretical characterizations of local minima of this procedure. We applied both techniques to many applications, including image segmentation, new view synthesis, superresolution, diagram recognition, parameter learning, texture restoration, and image deconvolution. For several applications we see that we are able to find the global minimum very efficiently, and considerably outperform the original roof duality approach. In comparison to existing techniques, such as graph cut, TRW, BP, ICM, and simulated annealing, we nearly always find a lower energy. 1.
Global Stereo Reconstruction under Second Order Smoothness Priors
"... Secondorder priors on the smoothness of 3D surfaces are a better model of typical scenes than firstorder priors. However, stereo reconstruction using global inference algorithms, such as graphcuts, has not been able to incorporate secondorder priors because the triple cliques needed to express t ..."
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Cited by 128 (8 self)
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Secondorder priors on the smoothness of 3D surfaces are a better model of typical scenes than firstorder priors. However, stereo reconstruction using global inference algorithms, such as graphcuts, has not been able to incorporate secondorder priors because the triple cliques needed to express them yield intractable (nonsubmodular) optimization problems. This paper shows that inference with triple cliques can be effectively optimized. Our optimization strategy is a development of recent extensions to αexpansion, based on the “QPBO ” algorithm [5, 14, 26]. The strategy is to repeatedly merge proposal depth maps using a novel extension of QPBO. Proposal depth maps can come from any source, for example frontoparallel planes as in αexpansion, or indeed any existing stereo algorithm, with arbitrary parameter settings. Experimental results demonstrate the usefulness of the secondorder prior and the efficacy of our optimization framework. An implementation of our stereo framework is available online [34].
Feature Correspondence via Graph Matching: Models and Global Optimization
"... Abstract. In this paper we present a new approach for establishing correspondences between sparse image features related by an unknown nonrigid mapping and corrupted by clutter and occlusion, such as points extracted from a pair of images containing a human figure in distinct poses. We formulate th ..."
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Cited by 121 (1 self)
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Abstract. In this paper we present a new approach for establishing correspondences between sparse image features related by an unknown nonrigid mapping and corrupted by clutter and occlusion, such as points extracted from a pair of images containing a human figure in distinct poses. We formulate this matching task as an energy minimization problem by defining a complex objective function of the appearance and the spatial arrangement of the features. Optimization of this energy is an instance of graph matching, which is in general a NPhard problem. We describe a novel graph matching optimization technique, which we refer to as dual decomposition (DD), and demonstrate on a variety of examples that this method outperforms existing graph matching algorithms. In the majority of our examples DD is able to find the global minimum within a minute. The ability to globally optimize the objective allows us to accurately learn the parameters of our matching model from training examples. We show on several matching tasks that our learned model yields results superior to those of stateoftheart methods. 1
Fusion Moves for Markov Random Field Optimization
"... The efficient application of graph cuts to Markov Random Fields (MRFs) with multiple discrete or continuous labels remains an open question. In this paper, we demonstrate one possible way of achieving this by using graph cuts to combine pairs of suboptimal labelings or solutions. We call this combi ..."
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Cited by 67 (5 self)
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The efficient application of graph cuts to Markov Random Fields (MRFs) with multiple discrete or continuous labels remains an open question. In this paper, we demonstrate one possible way of achieving this by using graph cuts to combine pairs of suboptimal labelings or solutions. We call this combination process the fusion move. By employing recently developed graph cut based algorithms (socalled QPBOgraph cut), the fusion move can efficiently combine two proposal labelings in a theoretically sound way, which is in practice often globally optimal. We demonstrate that fusion moves generalize many previous graph cut approaches, which allows them to be used as building block within a broader variety of optimization schemes than were considered before. In particular, we propose new optimization schemes for computer vision MRFs with applications to image restoration, stereo, and optical flow, among others. Within these schemes the fusion moves are used 1) for the parallelization of MRF optimization into several threads; 2) for fast MRF optimization by combining cheaptocompute solutions; and 3) for the optimization of highly nonconvex continuouslabeled MRFs with 2D labels. Our final example is a nonvision MRF concerned with cartographic label placement, where fusion moves can be used to improve the performance of a standard inference method (loopy belief propagation).
FusionFlow: DiscreteContinuous Optimization for Optical Flow Estimation
, 2008
"... Accurate estimation of optical flow is a challenging task, which often requires addressing difficult energy optimization problems. To solve them, most topperforming methods rely on continuous optimization algorithms. The modeling accuracy of the energy in this case is often traded for its tractabil ..."
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Cited by 58 (7 self)
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Accurate estimation of optical flow is a challenging task, which often requires addressing difficult energy optimization problems. To solve them, most topperforming methods rely on continuous optimization algorithms. The modeling accuracy of the energy in this case is often traded for its tractability. This is in contrast to the related problem of narrowbaseline stereo matching, where the topperforming methods employ powerful discrete optimization algorithms such as graph cuts and messagepassing to optimize highly nonconvex energies. In this paper, we demonstrate how similar nonconvex energies can be formulated and optimized discretely in the context of optical flow estimation. Starting with a set of candidate solutions that are produced by fast continuous flow estimation algorithms, the proposed method iteratively fuses these candidate solutions by the computation of minimum cuts on graphs. The obtained continuousvalued fusion result is then further improved using local gradient descent. Experimentally, we demonstrate that the proposed energy is an accurate model and that the proposed discretecontinuous optimization scheme not only finds lower energy solutions than traditional discrete or continuous optimization techniques, but also leads to flow estimates that outperform the current stateoftheart.
Halfintegrality based algorithms for cosegmentation of images
 In CVPR
, 2009
"... We study the cosegmentation problem where the objective is to segment the same object (i.e., region) from a pair of images. The segmentation for each image can be cast using a partitioning/segmentation function with an additional constraint that seeks to make the histograms of the segmented regions ..."
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Cited by 52 (4 self)
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We study the cosegmentation problem where the objective is to segment the same object (i.e., region) from a pair of images. The segmentation for each image can be cast using a partitioning/segmentation function with an additional constraint that seeks to make the histograms of the segmented regions (based on intensity and texture features) similar. Using Markov Random Field (MRF) energy terms for the simultaneous segmentation of the images together with histogram consistency requirements using the squared L2 (rather than L1) distance, after linearization and adjustments, yields an optimization model with some interesting combinatorial properties. We discuss these properties which are closely related to certain relaxation strategies recently introduced in computer vision. Finally, we show experimental results of the proposed approach. 1.
On Partial Optimality in Multilabel MRFs
, 2008
"... We consider the problem of optimizing multilabel MRFs, which is in general NPhard and ubiquitous in lowlevel computer vision. One approach for its solution is to formulate it as an integer linear programming and relax the integrality constraints. The approach we consider in this paper is to first ..."
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Cited by 35 (5 self)
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We consider the problem of optimizing multilabel MRFs, which is in general NPhard and ubiquitous in lowlevel computer vision. One approach for its solution is to formulate it as an integer linear programming and relax the integrality constraints. The approach we consider in this paper is to first convert the multilabel MRF into an equivalent binarylabel MRF and then to relax it. The resulting relaxation can be efficiently solved using a maximum flow algorithm. Its solution provides us with a partially optimal labelling of the binary variables. This partial labelling is then easily transferred to the multilabel problem. We study the theoretical properties of the new relaxation and compare it with the standard one. Specifically, we compare tightness, and characterize a subclass of problems where the two relaxations coincide. We propose several combined algorithms based on the technique and demonstrate their performance on challenging computer vision problems.
Transformation of General Binary MRF Minimization to the First Order Case
 IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI
, 2011
"... Abstract—We introduce a transformation of general higherorder Markov random field with binary labels into a firstorder one that has the same minima as the original. Moreover, we formalize a framework for approximately minimizing higherorder multilabel MRF energies that combines the new reduction ..."
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Cited by 29 (3 self)
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Abstract—We introduce a transformation of general higherorder Markov random field with binary labels into a firstorder one that has the same minima as the original. Moreover, we formalize a framework for approximately minimizing higherorder multilabel MRF energies that combines the new reduction with the fusionmove and QPBO algorithms. While many computer vision problems today are formulated as energy minimization problems, they have mostly been limited to using firstorder energies, which consist of unary and pairwise clique potentials, with a few exceptions that consider triples. This is because of the lack of efficient algorithms to optimize energies with higherorder interactions. Our algorithm challenges this restriction that limits the representational power of the models so that higherorder energies can be used to capture the rich statistics of natural scenes. We also show that some minimization methods can be considered special cases of the present framework, as well as comparing the new method experimentally with other such techniques. Index Terms—Energy minimization, pseudoBoolean function, higher order MRFs, graph cuts. F 1
Fast Global Optimization of Curvature
"... Two challenges in computer vision are to accommodate noisy data and missing data. Many problems in computer vision, such as segmentation, filtering, stereo, reconstruction, inpainting and optical flow seek solutions that match the data while satisfying an additional regularization, such as total var ..."
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Cited by 28 (3 self)
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Two challenges in computer vision are to accommodate noisy data and missing data. Many problems in computer vision, such as segmentation, filtering, stereo, reconstruction, inpainting and optical flow seek solutions that match the data while satisfying an additional regularization, such as total variation or boundary length. A regularization which has received less attention is to minimize the curvature of the solution. One reason why this regularization has received less attention is due to the difficulty in finding an optimal solution to this image model, since many existing methods are complicated, slow and/or provide a suboptimal solution. Following the recent progress of Schoenemann et al. [28], we provide a simple formulation of curvature regularization which admits a fast optimization which gives globally optimal solutions in practice. We demonstrate the effectiveness of this method by applying this curvature regularization to image segmentation. 1.